function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta.
%               You should set J to the cost.
%               Compute the partial derivatives and set grad to the partial
%               derivatives of the cost w.r.t. each parameter in theta



h = sigmoid(X*theta); %每一行数据的假设值
t_theta = theta(2:size(theta,1));
J = -1*(log(h)'*y+log(1-h)'*(1-y))/m+lambda*t_theta'*t_theta/(2*m);

grad = ((h.-y)'*X)'/m;

for i = 2:size(theta)
  grad(i) = grad(i)+ lambda*theta(i)/m;
end


% =============================================================

end
